LMFDB - Embedded newform 690.2.i.f.47.7

Newspace parameters

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.7
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.7

$q$-expansion

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.12660 - 1.31559i) q^{3} -1.00000i q^{4} +(-0.192443 + 2.22777i) q^{5} +(0.133641 + 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.461565 - 2.96428i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.12660 - 1.31559i) q^{3} -1.00000i q^{4} +(-0.192443 + 2.22777i) q^{5} +(0.133641 + 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.461565 - 2.96428i) q^{9} +(-1.43919 - 1.71135i) q^{10} +2.97195i q^{11} +(-1.31559 - 1.12660i) q^{12} +(-1.33263 + 1.33263i) q^{13} -2.77200 q^{14} +(2.71403 + 2.76297i) q^{15} -1.00000 q^{16} +(0.217329 - 0.217329i) q^{17} +(2.42244 + 1.76969i) q^{18} +6.42606i q^{19} +(2.22777 + 0.192443i) q^{20} +(4.78694 - 0.370453i) q^{21} +(-2.10149 - 2.10149i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(1.72689 - 0.133641i) q^{24} +(-4.92593 - 0.857436i) q^{25} -1.88462i q^{26} +(-4.41978 - 2.73231i) q^{27} +(1.96010 - 1.96010i) q^{28} -1.22002 q^{29} +(-3.87283 - 0.0346053i) q^{30} +6.33502 q^{31} +(0.707107 - 0.707107i) q^{32} +(3.90988 + 3.34819i) q^{33} +0.307349i q^{34} +(-4.74387 + 3.98945i) q^{35} +(-2.96428 + 0.461565i) q^{36} +(1.43305 + 1.43305i) q^{37} +(-4.54391 - 4.54391i) q^{38} +(0.251863 + 3.25453i) q^{39} +(-1.71135 + 1.43919i) q^{40} -3.04579i q^{41} +(-3.12292 + 3.64682i) q^{42} +(-1.80190 + 1.80190i) q^{43} +2.97195 q^{44} +(6.69256 - 0.457809i) q^{45} +1.00000 q^{46} +(0.199419 - 0.199419i) q^{47} +(-1.12660 + 1.31559i) q^{48} +0.683996i q^{49} +(4.08946 - 2.87686i) q^{50} +(-0.0410744 - 0.530758i) q^{51} +(1.33263 + 1.33263i) q^{52} +(9.17886 + 9.17886i) q^{53} +(5.05729 - 1.19322i) q^{54} +(-6.62083 - 0.571930i) q^{55} +2.77200i q^{56} +(8.45408 + 7.23957i) q^{57} +(0.862686 - 0.862686i) q^{58} +9.43000 q^{59} +(2.76297 - 2.71403i) q^{60} +5.57225 q^{61} +(-4.47954 + 4.47954i) q^{62} +(4.90558 - 6.71501i) q^{63} +1.00000i q^{64} +(-2.71234 - 3.22525i) q^{65} +(-5.13223 + 0.397175i) q^{66} +(9.41060 + 9.41060i) q^{67} +(-0.217329 - 0.217329i) q^{68} +(-1.72689 + 0.133641i) q^{69} +(0.533451 - 6.17539i) q^{70} -7.64983i q^{71} +(1.76969 - 2.42244i) q^{72} +(-4.05708 + 4.05708i) q^{73} -2.02664 q^{74} +(-6.67757 + 5.51453i) q^{75} +6.42606 q^{76} +(-5.82533 + 5.82533i) q^{77} +(-2.47940 - 2.12321i) q^{78} -14.4298i q^{79} +(0.192443 - 2.22777i) q^{80} +(-8.57391 + 2.73642i) q^{81} +(2.15370 + 2.15370i) q^{82} +(-12.1736 - 12.1736i) q^{83} +(-0.370453 - 4.78694i) q^{84} +(0.442336 + 0.525982i) q^{85} -2.54827i q^{86} +(-1.37447 + 1.60505i) q^{87} +(-2.10149 + 2.10149i) q^{88} -2.45643 q^{89} +(-4.40864 + 5.05608i) q^{90} -5.22418 q^{91} +(-0.707107 + 0.707107i) q^{92} +(7.13701 - 8.33431i) q^{93} +0.282021i q^{94} +(-14.3158 - 1.23665i) q^{95} +(-0.133641 - 1.72689i) q^{96} +(8.98748 + 8.98748i) q^{97} +(-0.483658 - 0.483658i) q^{98} +(8.80970 - 1.37175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) $	$ 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.12660	−	1.31559i	0.650440	−	0.759557i
$3$	1.12660	−	1.31559i	0.650440	−	0.759557i
$4$		−	1.00000i		−	0.500000i
$5$	−0.192443	+	2.22777i	−0.0860629	+	0.996290i
$5$	−0.192443	+	2.22777i	−0.0860629	+	0.996290i
$6$	0.133641	+	1.72689i	0.0545587	+	0.704999i
$7$	1.96010	+	1.96010i	0.740849	+	0.740849i	0.972741	−	0.231893i	$-0.0744918\pi$
$7$	1.96010	+	1.96010i	0.740849	+	0.740849i	−0.231893	+	0.972741i	$0.574492\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.461565	−	2.96428i	−0.153855	−	0.988093i
$10$	−1.43919	−	1.71135i	−0.455113	−	0.541176i
$11$			2.97195i			0.896078i	0.894014	+	0.448039i	$0.147877\pi$
$11$			2.97195i			0.896078i	−0.894014	+	0.448039i	$0.852123\pi$
$12$	−1.31559	−	1.12660i	−0.379779	−	0.325220i
$13$	−1.33263	+	1.33263i	−0.369605	+	0.369605i	−0.867333	−	0.497728i	$-0.834168\pi$
$13$	−1.33263	+	1.33263i	−0.369605	+	0.369605i	0.497728	+	0.867333i	$0.334168\pi$
$14$	−2.77200			−0.740849
$15$	2.71403	+	2.76297i	0.700761	+	0.713397i
$16$	−1.00000			−0.250000
$17$	0.217329	−	0.217329i	0.0527100	−	0.0527100i	−0.680260	−	0.732970i	$-0.738133\pi$
$17$	0.217329	−	0.217329i	0.0527100	−	0.0527100i	0.732970	+	0.680260i	$0.238133\pi$
$18$	2.42244	+	1.76969i	0.570974	+	0.417119i
$19$			6.42606i			1.47424i	0.675762	+	0.737120i	$0.263815\pi$
$19$			6.42606i			1.47424i	−0.675762	+	0.737120i	$0.736185\pi$
$20$	2.22777	+	0.192443i	0.498145	+	0.0430315i
$21$	4.78694	−	0.370453i	1.04459	−	0.0808394i
$22$	−2.10149	−	2.10149i	−0.448039	−	0.448039i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	1.72689	−	0.133641i	0.352499	−	0.0272793i
$25$	−4.92593	−	0.857436i	−0.985186	−	0.171487i
$26$		−	1.88462i		−	0.369605i
$27$	−4.41978	−	2.73231i	−0.850587	−	0.525834i
$28$	1.96010	−	1.96010i	0.370424	−	0.370424i
$29$	−1.22002			−0.226552			−0.113276	−	0.993564i	$-0.536134\pi$
$29$	−1.22002			−0.226552			−0.113276	+	0.993564i	$0.536134\pi$
$30$	−3.87283	−	0.0346053i	−0.707079	−	0.00631804i
$31$	6.33502			1.13780			0.568902	−	0.822405i	$-0.307368\pi$
$31$	6.33502			1.13780			0.568902	+	0.822405i	$0.307368\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.90988	+	3.34819i	0.680623	+	0.582845i
$34$			0.307349i			0.0527100i
$35$	−4.74387	+	3.98945i	−0.801860	+	0.674340i
$36$	−2.96428	+	0.461565i	−0.494047	+	0.0769276i
$37$	1.43305	+	1.43305i	0.235592	+	0.235592i	0.815022	−	0.579430i	$-0.196725\pi$
$37$	1.43305	+	1.43305i	0.235592	+	0.235592i	−0.579430	+	0.815022i	$0.696725\pi$
$38$	−4.54391	−	4.54391i	−0.737120	−	0.737120i
$39$	0.251863	+	3.25453i	0.0403303	+	0.521142i
$40$	−1.71135	+	1.43919i	−0.270588	+	0.227557i
$41$		−	3.04579i		−	0.475672i	−0.971305	−	0.237836i	$-0.923562\pi$
$41$		−	3.04579i		−	0.475672i	0.971305	−	0.237836i	$-0.0764380\pi$
$42$	−3.12292	+	3.64682i	−0.481878	+	0.562717i
$43$	−1.80190	+	1.80190i	−0.274786	+	0.274786i	−0.831024	−	0.556237i	$-0.812245\pi$
$43$	−1.80190	+	1.80190i	−0.274786	+	0.274786i	0.556237	+	0.831024i	$0.312245\pi$
$44$	2.97195			0.448039
$45$	6.69256	−	0.457809i	0.997669	−	0.0682461i
$46$	1.00000			0.147442
$47$	0.199419	−	0.199419i	0.0290883	−	0.0290883i	−0.692413	−	0.721501i	$-0.743452\pi$
$47$	0.199419	−	0.199419i	0.0290883	−	0.0290883i	0.721501	+	0.692413i	$0.243452\pi$
$48$	−1.12660	+	1.31559i	−0.162610	+	0.189889i
$49$			0.683996i			0.0977137i
$50$	4.08946	−	2.87686i	0.578337	−	0.406850i
$51$	−0.0410744	−	0.530758i	−0.00575157	−	0.0743210i
$52$	1.33263	+	1.33263i	0.184803	+	0.184803i
$53$	9.17886	+	9.17886i	1.26081	+	1.26081i	0.950699	+	0.310114i	$0.100367\pi$
$53$	9.17886	+	9.17886i	1.26081	+	1.26081i	0.310114	+	0.950699i	$0.399633\pi$
$54$	5.05729	−	1.19322i	0.688211	−	0.162377i
$55$	−6.62083	−	0.571930i	−0.892753	−	0.0771191i
$56$			2.77200i			0.370424i
$57$	8.45408	+	7.23957i	1.11977	+	0.958905i
$58$	0.862686	−	0.862686i	0.113276	−	0.113276i
$59$	9.43000			1.22768			0.613841	−	0.789430i	$-0.289624\pi$
$59$	9.43000			1.22768			0.613841	+	0.789430i	$0.289624\pi$
$60$	2.76297	−	2.71403i	0.356698	−	0.350380i
$61$	5.57225			0.713454			0.356727	−	0.934209i	$-0.383893\pi$
$61$	5.57225			0.713454			0.356727	+	0.934209i	$0.383893\pi$
$62$	−4.47954	+	4.47954i	−0.568902	+	0.568902i
$63$	4.90558	−	6.71501i	0.618044	−	0.846011i
$64$			1.00000i			0.125000i
$65$	−2.71234	−	3.22525i	−0.336425	−	0.400043i
$66$	−5.13223	+	0.397175i	−0.631734	+	0.0488888i
$67$	9.41060	+	9.41060i	1.14969	+	1.14969i	0.986614	+	0.163074i	$0.0521410\pi$
$67$	9.41060	+	9.41060i	1.14969	+	1.14969i	0.163074	+	0.986614i	$0.447859\pi$
$68$	−0.217329	−	0.217329i	−0.0263550	−	0.0263550i
$69$	−1.72689	+	0.133641i	−0.207893	+	0.0160885i
$70$	0.533451	−	6.17539i	0.0637596	−	0.738100i
$71$		−	7.64983i		−	0.907868i	−0.891035	−	0.453934i	$-0.850020\pi$
$71$		−	7.64983i		−	0.907868i	0.891035	−	0.453934i	$-0.149980\pi$
$72$	1.76969	−	2.42244i	0.208560	−	0.285487i
$73$	−4.05708	+	4.05708i	−0.474845	+	0.474845i	−0.903479	−	0.428633i	$-0.858995\pi$
$73$	−4.05708	+	4.05708i	−0.474845	+	0.474845i	0.428633	+	0.903479i	$0.358995\pi$
$74$	−2.02664			−0.235592
$75$	−6.67757	+	5.51453i	−0.771059	+	0.636763i
$76$	6.42606			0.737120
$77$	−5.82533	+	5.82533i	−0.663858	+	0.663858i
$78$	−2.47940	−	2.12321i	−0.280736	−	0.240406i
$79$		−	14.4298i		−	1.62348i	−0.584018	−	0.811741i	$-0.698520\pi$
$79$		−	14.4298i		−	1.62348i	0.584018	−	0.811741i	$-0.301480\pi$
$80$	0.192443	−	2.22777i	0.0215157	−	0.249072i
$81$	−8.57391	+	2.73642i	−0.952657	+	0.304047i
$82$	2.15370	+	2.15370i	0.237836	+	0.237836i
$83$	−12.1736	−	12.1736i	−1.33622	−	1.33622i	−0.899688	−	0.436533i	$-0.856206\pi$
$83$	−12.1736	−	12.1736i	−1.33622	−	1.33622i	−0.436533	−	0.899688i	$-0.643794\pi$
$84$	−0.370453	−	4.78694i	−0.0404197	−	0.522297i
$85$	0.442336	+	0.525982i	0.0479780	+	0.0570508i
$86$		−	2.54827i		−	0.274786i
$87$	−1.37447	+	1.60505i	−0.147359	+	0.172080i
$88$	−2.10149	+	2.10149i	−0.224019	+	0.224019i
$89$	−2.45643			−0.260381			−0.130191	−	0.991489i	$-0.541559\pi$
$89$	−2.45643			−0.260381			−0.130191	+	0.991489i	$0.541559\pi$
$90$	−4.40864	+	5.05608i	−0.464711	+	0.532957i
$91$	−5.22418			−0.547643
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	7.13701	−	8.33431i	0.740073	−	0.864227i
$94$			0.282021i			0.0290883i
$95$	−14.3158	−	1.23665i	−1.46877	−	0.126877i
$96$	−0.133641	−	1.72689i	−0.0136397	−	0.176250i
$97$	8.98748	+	8.98748i	0.912541	+	0.912541i	0.996472	−	0.0839309i	$-0.0267475\pi$
$97$	8.98748	+	8.98748i	0.912541	+	0.912541i	−0.0839309	+	0.996472i	$0.526748\pi$
$98$	−0.483658	−	0.483658i	−0.0488568	−	0.0488568i
$99$	8.80970	−	1.37175i	0.885409	−	0.137866i
$100$	−0.857436	+	4.92593i	−0.0857436	+	0.492593i
$101$		−	3.00976i		−	0.299482i	−0.988725	−	0.149741i	$-0.952156\pi$
$101$		−	3.00976i		−	0.299482i	0.988725	−	0.149741i	$-0.0478440\pi$
$102$	0.404346	+	0.346258i	0.0400363	+	0.0342847i
$103$	−1.81831	+	1.81831i	−0.179163	+	0.179163i	−0.790991	−	0.611828i	$-0.790435\pi$
$103$	−1.81831	+	1.81831i	−0.179163	+	0.179163i	0.611828	+	0.790991i	$0.290435\pi$
$104$	−1.88462			−0.184803
$105$	−0.0959261	+	10.7355i	−0.00936143	+	1.04768i
$106$	−12.9809			−1.26081
$107$	−10.1552	+	10.1552i	−0.981744	+	0.981744i	−0.999836	−	0.0180921i	$-0.994241\pi$
$107$	−10.1552	+	10.1552i	−0.981744	+	0.981744i	0.0180921	+	0.999836i	$0.494241\pi$
$108$	−2.73231	+	4.41978i	−0.262917	+	0.425294i
$109$		−	3.22282i		−	0.308690i	−0.988017	−	0.154345i	$-0.950673\pi$
$109$		−	3.22282i		−	0.308690i	0.988017	−	0.154345i	$-0.0493268\pi$
$110$	5.08605	−	4.27722i	0.484936	−	0.407817i
$111$	3.49978	−	0.270842i	0.332184	−	0.0257072i
$112$	−1.96010	−	1.96010i	−0.185212	−	0.185212i
$113$	−3.72990	−	3.72990i	−0.350880	−	0.350880i	0.509557	−	0.860437i	$-0.329809\pi$
$113$	−3.72990	−	3.72990i	−0.350880	−	0.350880i	−0.860437	+	0.509557i	$0.829809\pi$
$114$	−11.0971	+	0.858785i	−1.03934	+	0.0804326i
$115$	1.71135	−	1.43919i	0.159584	−	0.134206i
$116$			1.22002i			0.113276i
$117$	4.56539	+	3.33519i	0.422070	+	0.308339i
$118$	−6.66802	+	6.66802i	−0.613841	+	0.613841i
$119$	0.851973			0.0781003
$120$	−0.0346053	+	3.87283i	−0.00315902	+	0.353539i
$121$	2.16749			0.197044
$122$	−3.94018	+	3.94018i	−0.356727	+	0.356727i
$123$	−4.00701	−	3.43137i	−0.361300	−	0.309396i
$124$		−	6.33502i		−	0.568902i
$125$	2.85813	−	10.8088i	0.255639	−	0.966772i
$126$	1.27946	+	8.21699i	0.113983	+	0.732028i
$127$	−9.95020	−	9.95020i	−0.882938	−	0.882938i	0.110895	−	0.993832i	$-0.464628\pi$
$127$	−9.95020	−	9.95020i	−0.882938	−	0.882938i	−0.993832	+	0.110895i	$0.964628\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.340552	+	4.40057i	0.0299840	+	0.387448i
$130$	4.19851	+	0.362682i	0.368234	+	0.0318093i
$131$		−	4.14724i		−	0.362346i	−0.983451	−	0.181173i	$-0.942011\pi$
$131$		−	4.14724i		−	0.362346i	0.983451	−	0.181173i	$-0.0579894\pi$
$132$	3.34819	−	3.90988i	0.291423	−	0.340311i
$133$	−12.5957	+	12.5957i	−1.09219	+	1.09219i
$134$	−13.3086			−1.14969
$135$	6.93752	−	9.32045i	0.597087	−	0.802177i
$136$	0.307349			0.0263550
$137$	6.71805	−	6.71805i	0.573962	−	0.573962i	−0.359271	−	0.933233i	$-0.616975\pi$
$137$	6.71805	−	6.71805i	0.573962	−	0.573962i	0.933233	+	0.359271i	$0.116975\pi$
$138$	1.12660	−	1.31559i	0.0959022	−	0.111991i
$139$		−	21.3303i		−	1.80921i	−0.426247	−	0.904607i	$-0.640165\pi$
$139$		−	21.3303i		−	1.80921i	0.426247	−	0.904607i	$-0.359835\pi$
$140$	3.98945	+	4.74387i	0.337170	+	0.400930i
$141$	−0.0376896	−	0.487019i	−0.00317404	−	0.0410144i
$142$	5.40925	+	5.40925i	0.453934	+	0.453934i
$143$	−3.96052	−	3.96052i	−0.331195	−	0.331195i
$144$	0.461565	+	2.96428i	0.0384638	+	0.247023i
$145$	0.234784	−	2.71793i	0.0194978	−	0.225712i
$146$		−	5.73758i		−	0.474845i
$147$	0.899860	+	0.770587i	0.0742192	+	0.0635569i
$148$	1.43305	−	1.43305i	0.117796	−	0.117796i
$149$	2.04707			0.167703			0.0838514	−	0.996478i	$-0.473278\pi$
$149$	2.04707			0.167703			0.0838514	+	0.996478i	$0.473278\pi$
$150$	0.822390	−	8.62112i	0.0671479	−	0.703911i
$151$	−2.64015			−0.214852			−0.107426	−	0.994213i	$-0.534261\pi$
$151$	−2.64015			−0.214852			−0.107426	+	0.994213i	$0.534261\pi$
$152$	−4.54391	+	4.54391i	−0.368560	+	0.368560i
$153$	−0.744535	−	0.543912i	−0.0601921	−	0.0439727i
$154$		−	8.23826i		−	0.663858i
$155$	−1.21913	+	14.1130i	−0.0979227	+	1.13358i
$156$	3.25453	−	0.251863i	0.260571	−	0.0201652i
$157$	0.750993	+	0.750993i	0.0599358	+	0.0599358i	0.736439	−	0.676504i	$-0.236506\pi$
$157$	0.750993	+	0.750993i	0.0599358	+	0.0599358i	−0.676504	+	0.736439i	$0.736506\pi$
$158$	10.2034	+	10.2034i	0.811741	+	0.811741i
$159$	22.4165	−	1.73477i	1.77774	−	0.137577i
$160$	1.43919	+	1.71135i	0.113778	+	0.135294i
$161$		−	2.77200i		−	0.218464i
$162$	4.12773	−	7.99761i	0.324305	−	0.628352i
$163$	6.60415	−	6.60415i	0.517277	−	0.517277i	−0.399469	−	0.916747i	$-0.630806\pi$
$163$	6.60415	−	6.60415i	0.517277	−	0.517277i	0.916747	+	0.399469i	$0.130806\pi$
$164$	−3.04579			−0.237836
$165$	−8.21143	+	8.06598i	−0.639259	+	0.627936i
$166$	17.2160			1.33622
$167$	5.25056	−	5.25056i	0.406300	−	0.406300i	−0.474146	−	0.880446i	$-0.657243\pi$
$167$	5.25056	−	5.25056i	0.406300	−	0.406300i	0.880446	+	0.474146i	$0.157243\pi$
$168$	3.64682	+	3.12292i	0.281359	+	0.240939i
$169$			9.44819i			0.726784i
$170$	−0.684704	−	0.0591471i	−0.0525144	−	0.00453638i
$171$	19.0487	−	2.96605i	1.45669	−	0.226819i
$172$	1.80190	+	1.80190i	0.137393	+	0.137393i
$173$	−16.1787	−	16.1787i	−1.23004	−	1.23004i	−0.963947	−	0.266093i	$-0.914267\pi$
$173$	−16.1787	−	16.1787i	−1.23004	−	1.23004i	−0.266093	−	0.963947i	$-0.585733\pi$
$174$	−0.163045	−	2.10684i	−0.0123604	−	0.159719i
$175$	−7.97466	−	11.3360i	−0.602828	−	0.856920i
$176$		−	2.97195i		−	0.224019i
$177$	10.6238	−	12.4060i	0.798533	−	0.932495i
$178$	1.73696	−	1.73696i	0.130191	−	0.130191i
$179$	12.6087			0.942418			0.471209	−	0.882022i	$-0.343818\pi$
$179$	12.6087			0.942418			0.471209	+	0.882022i	$0.343818\pi$
$180$	−0.457809	−	6.69256i	−0.0341230	−	0.498834i
$181$	−1.75381			−0.130360			−0.0651799	−	0.997874i	$-0.520762\pi$
$181$	−1.75381			−0.130360			−0.0651799	+	0.997874i	$0.520762\pi$
$182$	3.69405	−	3.69405i	0.273822	−	0.273822i
$183$	6.27767	−	7.33081i	0.464059	−	0.541909i
$184$		−	1.00000i		−	0.0737210i
$185$	−3.46829	+	2.91673i	−0.254994	+	0.214442i
$186$	0.846618	+	10.9399i	0.0620771	+	0.802150i
$187$	0.645891	+	0.645891i	0.0472322	+	0.0472322i
$188$	−0.199419	−	0.199419i	−0.0145441	−	0.0145441i
$189$	−3.30761	−	14.0188i	−0.240593	−	1.01972i
$190$	10.9972	−	9.24836i	0.797824	−	0.670946i
$191$		−	26.9285i		−	1.94848i	−0.225520	−	0.974238i	$-0.572408\pi$
$191$		−	26.9285i		−	1.94848i	0.225520	−	0.974238i	$-0.427592\pi$
$192$	1.31559	+	1.12660i	0.0949447	+	0.0813050i
$193$	−10.9317	+	10.9317i	−0.786878	+	0.786878i	−0.980981	−	0.194103i	$-0.937820\pi$
$193$	−10.9317	+	10.9317i	−0.786878	+	0.786878i	0.194103	+	0.980981i	$0.437820\pi$
$194$	−12.7102			−0.912541
$195$	−7.29883	−	0.0652180i	−0.522680	−	0.00467036i
$196$	0.683996			0.0488568
$197$	−1.97929	+	1.97929i	−0.141019	+	0.141019i	−0.774092	−	0.633073i	$-0.781793\pi$
$197$	−1.97929	+	1.97929i	−0.141019	+	0.141019i	0.633073	+	0.774092i	$0.281793\pi$
$198$	−5.25943	+	7.19938i	−0.373771	+	0.511637i
$199$		−	15.8892i		−	1.12636i	−0.826336	−	0.563178i	$-0.809579\pi$
$199$		−	15.8892i		−	1.12636i	0.826336	−	0.563178i	$-0.190421\pi$
$200$	−2.87686	−	4.08946i	−0.203425	−	0.289168i
$201$	22.9825	−	1.77857i	1.62106	−	0.125451i
$202$	2.12822	+	2.12822i	0.149741	+	0.149741i
$203$	−2.39137	−	2.39137i	−0.167841	−	0.167841i
$204$	−0.530758	+	0.0410744i	−0.0371605	+	0.00287579i
$205$	6.78531	+	0.586139i	0.473907	+	0.0409377i
$206$		−	2.57147i		−	0.179163i
$207$	−1.76969	+	2.42244i	−0.123002	+	0.168371i
$208$	1.33263	−	1.33263i	0.0924013	−	0.0924013i
$209$	−19.0980			−1.32103
$210$	−7.52331	−	7.65897i	−0.519158	−	0.528519i
$211$	11.3907			0.784169			0.392085	−	0.919929i	$-0.371754\pi$
$211$	11.3907			0.784169			0.392085	+	0.919929i	$0.371754\pi$
$212$	9.17886	−	9.17886i	0.630407	−	0.630407i
$213$	−10.0641	−	8.61826i	−0.689578	−	0.590514i
$214$		−	14.3617i		−	0.981744i
$215$	−3.66745	−	4.36097i	−0.250118	−	0.297416i
$216$	−1.19322	−	5.05729i	−0.0811884	−	0.344105i
$217$	12.4173	+	12.4173i	0.842941	+	0.842941i
$218$	2.27888	+	2.27888i	0.154345	+	0.154345i
$219$	0.766775	+	9.90815i	0.0518138	+	0.669531i
$220$	−0.571930	+	6.62083i	−0.0385595	+	0.446377i
$221$			0.579238i			0.0389638i
$222$	−2.28320	+	2.66623i	−0.153239	+	0.178946i
$223$	−10.4680	+	10.4680i	−0.700989	+	0.700989i	−0.964623	−	0.263634i	$-0.915079\pi$
$223$	−10.4680	+	10.4680i	−0.700989	+	0.700989i	0.263634	+	0.964623i	$0.415079\pi$
$224$	2.77200			0.185212
$225$	−0.268041	+	14.9976i	−0.0178694	+	0.999840i
$226$	5.27488			0.350880
$227$	−16.1663	+	16.1663i	−1.07299	+	1.07299i	−0.0758747	+	0.997117i	$0.524175\pi$
$227$	−16.1663	+	16.1663i	−1.07299	+	1.07299i	−0.997117	+	0.0758747i	$0.975825\pi$
$228$	7.23957	−	8.45408i	0.479453	−	0.559885i
$229$		−	16.0298i		−	1.05928i	−0.848224	−	0.529638i	$-0.822328\pi$
$229$		−	16.0298i		−	1.05928i	0.848224	−	0.529638i	$-0.177672\pi$
$230$	−0.192443	+	2.22777i	−0.0126893	+	0.146895i
$231$	1.10097	+	14.2266i	0.0724384	+	0.936038i
$232$	−0.862686	−	0.862686i	−0.0566381	−	0.0566381i
$233$	−4.14654	−	4.14654i	−0.271649	−	0.271649i	0.558115	−	0.829764i	$-0.311525\pi$
$233$	−4.14654	−	4.14654i	−0.271649	−	0.271649i	−0.829764	+	0.558115i	$0.811525\pi$
$234$	−5.58655	+	0.869877i	−0.365204	+	0.0568657i
$235$	0.405884	+	0.482637i	0.0264769	+	0.0314838i
$236$		−	9.43000i		−	0.613841i
$237$	−18.9838	−	16.2566i	−1.23313	−	1.05598i
$238$	−0.602436	+	0.602436i	−0.0390501	+	0.0390501i
$239$	29.7656			1.92538			0.962690	−	0.270608i	$-0.0872246\pi$
$239$	29.7656			1.92538			0.962690	+	0.270608i	$0.0872246\pi$
$240$	−2.71403	−	2.76297i	−0.175190	−	0.178349i
$241$	−18.1553			−1.16949			−0.584743	−	0.811219i	$-0.698805\pi$
$241$	−18.1553			−1.16949			−0.584743	+	0.811219i	$0.698805\pi$
$242$	−1.53265	+	1.53265i	−0.0985222	+	0.0985222i
$243$	−6.05932	+	14.3626i	−0.388706	+	0.921362i
$244$		−	5.57225i		−	0.356727i
$245$	−1.52379	−	0.131630i	−0.0973512	−	0.00840953i
$246$	5.25973	−	0.407041i	0.335348	−	0.0259520i
$247$	−8.56357	−	8.56357i	−0.544887	−	0.544887i
$248$	4.47954	+	4.47954i	0.284451	+	0.284451i
$249$	−29.7301	+	2.30076i	−1.88407	+	0.145805i
$250$	5.62200	+	9.66401i	0.355567	+	0.611206i
$251$			19.1213i			1.20693i	0.797390	+	0.603464i	$0.206213\pi$
$251$			19.1213i			1.20693i	−0.797390	+	0.603464i	$0.793787\pi$
$252$	−6.71501	−	4.90558i	−0.423006	−	0.309022i
$253$	2.10149	−	2.10149i	0.132119	−	0.132119i
$254$	14.0717			0.882938
$255$	1.19031	+	0.0106359i	0.0745402	+	0.000666048i
$256$	1.00000			0.0625000
$257$	17.0084	−	17.0084i	1.06096	−	1.06096i	0.0629387	−	0.998017i	$-0.479953\pi$
$257$	17.0084	−	17.0084i	1.06096	−	1.06096i	0.998017	−	0.0629387i	$-0.0200473\pi$
$258$	−3.35248	−	2.87086i	−0.208716	−	0.178732i
$259$			5.61785i			0.349076i
$260$	−3.22525	+	2.71234i	−0.200022	+	0.168212i
$261$	0.563120	+	3.61649i	0.0348563	+	0.223855i
$262$	2.93254	+	2.93254i	0.181173	+	0.181173i
$263$	12.3574	+	12.3574i	0.761992	+	0.761992i	0.976682	−	0.214690i	$-0.0688741\pi$
$263$	12.3574	+	12.3574i	0.761992	+	0.761992i	−0.214690	+	0.976682i	$0.568874\pi$
$264$	0.397175	+	5.13223i	0.0244444	+	0.315867i
$265$	−22.2148	+	18.6820i	−1.36464	+	1.14763i
$266$		−	17.8131i		−	1.09219i
$267$	−2.76740	+	3.23166i	−0.169362	+	0.197774i
$268$	9.41060	−	9.41060i	0.574844	−	0.574844i
$269$	20.0999			1.22552			0.612758	−	0.790271i	$-0.290060\pi$
$269$	20.0999			1.22552			0.612758	+	0.790271i	$0.290060\pi$
$270$	1.68498	+	11.4961i	0.102545	+	0.699632i
$271$	−27.8676			−1.69284			−0.846419	−	0.532518i	$-0.821246\pi$
$271$	−27.8676			−1.69284			−0.846419	+	0.532518i	$0.821246\pi$
$272$	−0.217329	+	0.217329i	−0.0131775	+	0.0131775i
$273$	−5.88554	+	6.87289i	−0.356209	+	0.415966i
$274$			9.50076i			0.573962i
$275$	2.54826	−	14.6396i	0.153666	−	0.882804i
$276$	0.133641	+	1.72689i	0.00804423	+	0.103946i
$277$	7.04930	+	7.04930i	0.423551	+	0.423551i	0.886424	−	0.462873i	$-0.153182\pi$
$277$	7.04930	+	7.04930i	0.423551	+	0.423551i	−0.462873	+	0.886424i	$0.653182\pi$
$278$	15.0828	+	15.0828i	0.904607	+	0.904607i
$279$	−2.92403	−	18.7788i	−0.175057	−	1.12426i
$280$	−6.17539	−	0.533451i	−0.369050	−	0.0318798i
$281$			15.7886i			0.941867i	0.882169	+	0.470934i	$0.156083\pi$
$281$			15.7886i			0.941867i	−0.882169	+	0.470934i	$0.843917\pi$
$282$	0.371025	+	0.317724i	0.0220942	+	0.0189202i
$283$	13.2043	−	13.2043i	0.784912	−	0.784912i	−0.195743	−	0.980655i	$-0.562712\pi$
$283$	13.2043	−	13.2043i	0.784912	−	0.784912i	0.980655	+	0.195743i	$0.0627118\pi$
$284$	−7.64983			−0.453934
$285$	−17.7550	+	17.4406i	−1.05172	+	1.03309i
$286$	5.60102			0.331195
$287$	5.97005	−	5.97005i	0.352401	−	0.352401i
$288$	−2.42244	−	1.76969i	−0.142744	−	0.104280i
$289$			16.9055i			0.994443i
$290$	1.75585	+	2.08788i	0.103107	+	0.122605i
$291$	21.9491	−	1.69860i	1.28668	−	0.0995740i
$292$	4.05708	+	4.05708i	0.237423	+	0.237423i
$293$	6.93824	+	6.93824i	0.405336	+	0.405336i	0.880109	−	0.474772i	$-0.157470\pi$
$293$	6.93824	+	6.93824i	0.405336	+	0.405336i	−0.474772	+	0.880109i	$0.657470\pi$
$294$	−1.18118	+	0.0914098i	−0.0688880	+	0.00533113i
$295$	−1.81473	+	21.0079i	−0.105658	+	1.22313i
$296$			2.02664i			0.117796i
$297$	8.12031	−	13.1354i	0.471188	−	0.762192i
$298$	−1.44750	+	1.44750i	−0.0838514	+	0.0838514i
$299$	1.88462			0.108991
$300$	5.51453	+	6.67757i	0.318382	+	0.385530i
$301$	−7.06380			−0.407150
$302$	1.86687	−	1.86687i	0.107426	−	0.107426i
$303$	−3.95962	−	3.39078i	−0.227474	−	0.194795i
$304$		−	6.42606i		−	0.368560i
$305$	−1.07234	+	12.4137i	−0.0614019	+	0.710807i
$306$	0.911070	−	0.141862i	0.0520824	−	0.00810970i
$307$	−8.38939	−	8.38939i	−0.478808	−	0.478808i	0.425943	−	0.904750i	$-0.359943\pi$
$307$	−8.38939	−	8.38939i	−0.478808	−	0.478808i	−0.904750	+	0.425943i	$0.859943\pi$
$308$	5.82533	+	5.82533i	0.331929	+	0.331929i
$309$	0.343654	+	4.44065i	0.0195498	+	0.252620i
$310$	−9.11733	−	10.8414i	−0.517830	−	0.615753i
$311$			22.7094i			1.28773i	0.765139	+	0.643865i	$0.222670\pi$
$311$			22.7094i			1.28773i	−0.765139	+	0.643865i	$0.777330\pi$
$312$	−2.12321	+	2.47940i	−0.120203	+	0.140368i
$313$	−19.0911	+	19.0911i	−1.07909	+	1.07909i	−0.0825035	+	0.996591i	$0.526292\pi$
$313$	−19.0911	+	19.0911i	−1.07909	+	1.07909i	−0.996591	+	0.0825035i	$0.973708\pi$
$314$	−1.06206			−0.0599358
$315$	14.0155	+	12.2208i	0.789681	+	0.688561i
$316$	−14.4298			−0.811741
$317$	−0.0275450	+	0.0275450i	−0.00154708	+	0.00154708i	−0.707880	−	0.706333i	$-0.750348\pi$
$317$	−0.0275450	+	0.0275450i	−0.00154708	+	0.00154708i	0.706333	+	0.707880i	$0.250348\pi$
$318$	−14.6242	+	17.0775i	−0.820084	+	0.957660i
$319$		−	3.62585i		−	0.203009i
$320$	−2.22777	−	0.192443i	−0.124536	−	0.0107579i
$321$	1.91931	+	24.8010i	0.107125	+	1.38426i
$322$	1.96010	+	1.96010i	0.109232	+	0.109232i
$323$	1.39657	+	1.39657i	0.0777072	+	0.0777072i
$324$	2.73642	+	8.57391i	0.152023	+	0.476329i
$325$	7.70709	−	5.42180i	0.427513	−	0.300747i
$326$			9.33968i			0.517277i
$327$	−4.23992	−	3.63082i	−0.234468	−	0.200785i
$328$	2.15370	−	2.15370i	0.118918	−	0.118918i
$329$	0.781764			0.0431000
$330$	0.102845	−	11.5099i	0.00566146	−	0.633597i
$331$	1.05162			0.0578024			0.0289012	−	0.999582i	$-0.490799\pi$
$331$	1.05162			0.0578024			0.0289012	+	0.999582i	$0.490799\pi$
$332$	−12.1736	+	12.1736i	−0.668111	+	0.668111i
$333$	3.58652	−	4.90941i	0.196540	−	0.269034i
$334$			7.42541i			0.406300i
$335$	−22.7757	+	19.1537i	−1.24437	+	1.04648i
$336$	−4.78694	+	0.370453i	−0.261149	+	0.0202099i
$337$	−10.0242	−	10.0242i	−0.546054	−	0.546054i	0.379243	−	0.925297i	$-0.376184\pi$
$337$	−10.0242	−	10.0242i	−0.546054	−	0.546054i	−0.925297	+	0.379243i	$0.876184\pi$
$338$	−6.68088	−	6.68088i	−0.363392	−	0.363392i
$339$	−9.10912	+	0.704939i	−0.494740	+	0.0382871i
$340$	0.525982	−	0.442336i	0.0285254	−	0.0239890i
$341$			18.8274i			1.01956i
$342$	−11.3721	+	15.5667i	−0.614934	+	0.841753i
$343$	12.3800	−	12.3800i	0.668458	−	0.668458i
$344$	−2.54827			−0.137393
$345$	0.0346053	−	3.87283i	0.00186309	−	0.208506i
$346$	22.8801			1.23004
$347$	18.2887	−	18.2887i	0.981790	−	0.981790i	−0.0180467	−	0.999837i	$-0.505745\pi$
$347$	18.2887	−	18.2887i	0.981790	−	0.981790i	0.999837	+	0.0180467i	$0.00574476\pi$
$348$	1.60505	+	1.37447i	0.0860398	+	0.0736794i
$349$		−	28.7041i		−	1.53649i	−0.640154	−	0.768247i	$-0.721129\pi$
$349$		−	28.7041i		−	1.53649i	0.640154	−	0.768247i	$-0.278871\pi$
$350$	13.6547	+	2.37681i	0.729874	+	0.127046i
$351$	9.53110	−	2.24877i	0.508732	−	0.120031i
$352$	2.10149	+	2.10149i	0.112010	+	0.112010i
$353$	10.4582	+	10.4582i	0.556631	+	0.556631i	0.928347	−	0.371715i	$-0.121230\pi$
$353$	10.4582	+	10.4582i	0.556631	+	0.556631i	−0.371715	+	0.928347i	$0.621230\pi$
$354$	1.26023	+	16.2846i	0.0669807	+	0.865514i
$355$	17.0421	+	1.47215i	0.904499	+	0.0781337i
$356$			2.45643i			0.130191i
$357$	0.959829	−	1.12085i	0.0507995	−	0.0593216i
$358$	−8.91569	+	8.91569i	−0.471209	+	0.471209i
$359$	−10.4419			−0.551105			−0.275552	−	0.961286i	$-0.588861\pi$
$359$	−10.4419			−0.551105			−0.275552	+	0.961286i	$0.588861\pi$
$360$	5.05608	+	4.40864i	0.266479	+	0.232356i
$361$	−22.2943			−1.17338
$362$	1.24013	−	1.24013i	0.0651799	−	0.0651799i
$363$	2.44188	−	2.85153i	0.128166	−	0.149667i
$364$			5.22418i			0.273822i
$365$	−8.25749	−	9.81900i	−0.432217	−	0.513950i
$366$	0.744681	+	9.62265i	0.0389251	+	0.502984i
$367$	11.3139	+	11.3139i	0.590580	+	0.590580i	0.937788	−	0.347208i	$-0.112870\pi$
$367$	11.3139	+	11.3139i	0.590580	+	0.590580i	−0.347208	+	0.937788i	$0.612870\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	−9.02856	+	1.40583i	−0.470008	+	0.0731846i
$370$	0.390012	−	4.51489i	0.0202758	−	0.234718i
$371$			35.9830i			1.86814i
$372$	−8.33431	−	7.13701i	−0.432114	−	0.370037i
$373$	−20.2494	+	20.2494i	−1.04847	+	1.04847i	−0.0497082	+	0.998764i	$0.515829\pi$
$373$	−20.2494	+	20.2494i	−1.04847	+	1.04847i	−0.998764	+	0.0497082i	$0.984171\pi$
$374$	−0.913428			−0.0472322
$375$	−11.0001	−	15.9373i	−0.568041	−	0.823000i
$376$	0.282021			0.0145441
$377$	1.62584	−	1.62584i	0.0837349	−	0.0837349i
$378$	12.2516	+	7.57398i	0.630157	+	0.389563i
$379$		−	31.4641i		−	1.61620i	−0.589042	−	0.808102i	$-0.700495\pi$
$379$		−	31.4641i		−	1.61620i	0.589042	−	0.808102i	$-0.299505\pi$
$380$	−1.23665	+	14.3158i	−0.0634387	+	0.734385i
$381$	−24.3003	+	1.88056i	−1.24494	+	0.0963438i
$382$	19.0413	+	19.0413i	0.974238	+	0.974238i
$383$	−5.10098	−	5.10098i	−0.260648	−	0.260648i	0.564669	−	0.825317i	$-0.309004\pi$
$383$	−5.10098	−	5.10098i	−0.260648	−	0.260648i	−0.825317	+	0.564669i	$0.809004\pi$
$384$	−1.72689	+	0.133641i	−0.0881249	+	0.00681983i
$385$	−11.8565	−	14.0985i	−0.604261	−	0.718529i
$386$		−	15.4597i		−	0.786878i
$387$	6.17302	+	4.50963i	0.313792	+	0.229237i
$388$	8.98748	−	8.98748i	0.456270	−	0.456270i
$389$	18.3647			0.931129			0.465565	−	0.885014i	$-0.345851\pi$
$389$	18.3647			0.931129			0.465565	+	0.885014i	$0.345851\pi$
$390$	5.20717	−	5.11493i	0.263675	−	0.259005i
$391$	−0.307349			−0.0155433
$392$	−0.483658	+	0.483658i	−0.0244284	+	0.0244284i
$393$	−5.45608	−	4.67226i	−0.275223	−	0.235685i
$394$		−	2.79914i		−	0.141019i
$395$	32.1463	+	2.77691i	1.61746	+	0.139722i
$396$	−1.37175	−	8.80970i	−0.0689331	−	0.442704i
$397$	−6.90089	−	6.90089i	−0.346346	−	0.346346i	0.512401	−	0.858746i	$-0.328756\pi$
$397$	−6.90089	−	6.90089i	−0.346346	−	0.346346i	−0.858746	+	0.512401i	$0.828756\pi$
$398$	11.2354	+	11.2354i	0.563178	+	0.563178i
$399$	2.38055	+	30.7612i	0.119177	+	1.53998i
$400$	4.92593	+	0.857436i	0.246297	+	0.0428718i
$401$		−	18.3481i		−	0.916261i	−0.888885	−	0.458131i	$-0.848519\pi$
$401$		−	18.3481i		−	0.916261i	0.888885	−	0.458131i	$-0.151481\pi$
$402$	−14.9934	+	17.5087i	−0.747803	+	0.873254i
$403$	−8.44225	+	8.44225i	−0.420538	+	0.420538i
$404$	−3.00976			−0.149741
$405$	−4.44613	−	19.6273i	−0.220930	−	0.975290i
$406$	3.38190			0.167841
$407$	−4.25896	+	4.25896i	−0.211109	+	0.211109i
$408$	0.346258	−	0.404346i	0.0171423	−	0.0200181i
$409$			15.8713i			0.784783i	0.919798	+	0.392392i	$0.128352\pi$
$409$			15.8713i			0.784783i	−0.919798	+	0.392392i	$0.871648\pi$
$410$	−5.21240	+	4.38348i	−0.257422	+	0.216485i
$411$	−1.26969	−	16.4067i	−0.0626292	−	0.809285i
$412$	1.81831	+	1.81831i	0.0895816	+	0.0895816i
$413$	18.4838	+	18.4838i	0.909526	+	0.909526i
$414$	−0.461565	−	2.96428i	−0.0226847	−	0.145686i
$415$	29.4626	−	24.7772i	1.44626	−	1.21626i
$416$			1.88462i			0.0924013i
$417$	−28.0620	−	24.0306i	−1.37420	−	1.17679i
$418$	13.5043	−	13.5043i	0.660517	−	0.660517i
$419$	−19.9035			−0.972349			−0.486175	−	0.873862i	$-0.661608\pi$
$419$	−19.9035			−0.972349			−0.486175	+	0.873862i	$0.661608\pi$
$420$	10.7355	+	0.0959261i	0.523838	+	0.00468071i
$421$	−9.07200			−0.442142			−0.221071	−	0.975258i	$-0.570955\pi$
$421$	−9.07200			−0.442142			−0.221071	+	0.975258i	$0.570955\pi$
$422$	−8.05445	+	8.05445i	−0.392085	+	0.392085i
$423$	−0.683180	−	0.499089i	−0.0332173	−	0.0242666i
$424$			12.9809i			0.630407i
$425$	−1.25689	+	0.884201i	−0.0609682	+	0.0428901i
$426$	13.2104	−	1.02233i	0.640046	−	0.0495320i
$427$	10.9222	+	10.9222i	0.528561	+	0.528561i
$428$	10.1552	+	10.1552i	0.490872	+	0.490872i
$429$	−9.67232	+	0.748525i	−0.466984	+	0.0361391i
$430$	5.67695	+	0.490395i	0.273767	+	0.0236489i
$431$			6.60333i			0.318071i	0.987273	+	0.159036i	$0.0508384\pi$
$431$			6.60333i			0.318071i	−0.987273	+	0.159036i	$0.949162\pi$
$432$	4.41978	+	2.73231i	0.212647	+	0.131458i
$433$	−2.95935	+	2.95935i	−0.142217	+	0.142217i	−0.774631	−	0.632414i	$-0.782064\pi$
$433$	−2.95935	+	2.95935i	−0.142217	+	0.142217i	0.632414	+	0.774631i	$0.282064\pi$
$434$	−17.5607			−0.842941
$435$	−3.31118	−	3.37089i	−0.158759	−	0.161622i
$436$	−3.22282			−0.154345
$437$	4.54391	−	4.54391i	0.217365	−	0.217365i
$438$	−7.54831	−	6.46393i	−0.360672	−	0.308858i
$439$		−	11.2528i		−	0.537068i	−0.963270	−	0.268534i	$-0.913461\pi$
$439$		−	11.2528i		−	0.537068i	0.963270	−	0.268534i	$-0.0865392\pi$
$440$	−4.27722	−	5.08605i	−0.203909	−	0.242468i
$441$	2.02756	−	0.315709i	0.0965503	−	0.0150338i
$442$	−0.409583	−	0.409583i	−0.0194819	−	0.0194819i
$443$	16.2317	+	16.2317i	0.771194	+	0.771194i	0.978315	−	0.207122i	$-0.0664096\pi$
$443$	16.2317	+	16.2317i	0.771194	+	0.771194i	−0.207122	+	0.978315i	$0.566410\pi$
$444$	−0.270842	−	3.49978i	−0.0128536	−	0.166092i
$445$	0.472722	−	5.47236i	0.0224092	−	0.259415i
$446$		−	14.8040i		−	0.700989i
$447$	2.30622	−	2.69311i	0.109081	−	0.127380i
$448$	−1.96010	+	1.96010i	−0.0926061	+	0.0926061i
$449$	3.47861			0.164166			0.0820828	−	0.996626i	$-0.473843\pi$
$449$	3.47861			0.164166			0.0820828	+	0.996626i	$0.473843\pi$
$450$	−10.4154	−	10.7944i	−0.490985	−	0.508855i
$451$	9.05193			0.426239
$452$	−3.72990	+	3.72990i	−0.175440	+	0.175440i
$453$	−2.97438	+	3.47336i	−0.139749	+	0.163193i
$454$		−	22.8625i		−	1.07299i
$455$	1.00535	−	11.6383i	0.0471318	−	0.545611i
$456$	0.858785	+	11.0971i	0.0402163	+	0.519669i
$457$	24.5212	+	24.5212i	1.14705	+	1.14705i	0.987129	+	0.159925i	$0.0511251\pi$
$457$	24.5212	+	24.5212i	1.14705	+	1.14705i	0.159925	+	0.987129i	$0.448875\pi$
$458$	11.3347	+	11.3347i	0.529638	+	0.529638i
$459$	−1.55436	+	0.366736i	−0.0725511	+	0.0171178i
$460$	−1.43919	−	1.71135i	−0.0671028	−	0.0797921i
$461$			7.06441i			0.329022i	0.986375	+	0.164511i	$0.0526047\pi$
$461$			7.06441i			0.329022i	−0.986375	+	0.164511i	$0.947395\pi$
$462$	−10.8382	−	9.28119i	−0.504238	−	0.431800i
$463$	4.91698	−	4.91698i	0.228512	−	0.228512i	−0.583559	−	0.812071i	$-0.698340\pi$
$463$	4.91698	−	4.91698i	0.228512	−	0.228512i	0.812071	+	0.583559i	$0.198340\pi$
$464$	1.22002			0.0566381
$465$	17.1935	+	17.5035i	0.797328	+	0.811705i
$466$	5.86409			0.271649
$467$	−0.279235	+	0.279235i	−0.0129214	+	0.0129214i	−0.713538	−	0.700617i	$-0.752908\pi$
$467$	−0.279235	+	0.279235i	−0.0129214	+	0.0129214i	0.700617	+	0.713538i	$0.252908\pi$
$468$	3.33519	−	4.56539i	0.154169	−	0.211035i
$469$			36.8915i			1.70349i
$470$	−0.628279	−	0.0542729i	−0.0289804	−	0.00250342i
$471$	1.83407	−	0.141935i	0.0845093	−	0.00654003i
$472$	6.66802	+	6.66802i	0.306920	+	0.306920i
$473$	−5.35515	−	5.35515i	−0.246230	−	0.246230i
$474$	24.9187	−	1.92841i	1.14455	−	0.0885750i
$475$	5.50994	−	31.6544i	0.252813	−	1.45240i
$476$		−	0.851973i		−	0.0390501i
$477$	22.9721	−	31.4454i	1.05182	−	1.43978i
$478$	−21.0475	+	21.0475i	−0.962690	+	0.962690i
$479$	19.9714			0.912518			0.456259	−	0.889847i	$-0.349189\pi$
$479$	19.9714			0.912518			0.456259	+	0.889847i	$0.349189\pi$
$480$	3.87283	+	0.0346053i	0.176770	+	0.00157951i
$481$	−3.81946			−0.174152
$482$	12.8377	−	12.8377i	0.584743	−	0.584743i
$483$	−3.64682	−	3.12292i	−0.165936	−	0.142098i
$484$		−	2.16749i		−	0.0985222i
$485$	−21.7516	+	18.2925i	−0.987691	+	0.830619i
$486$	−5.87131	−	14.4405i	−0.266328	−	0.655034i
$487$	−1.40410	−	1.40410i	−0.0636258	−	0.0636258i	0.674578	−	0.738204i	$-0.264326\pi$
$487$	−1.40410	−	1.40410i	−0.0636258	−	0.0636258i	−0.738204	+	0.674578i	$0.764326\pi$
$488$	3.94018	+	3.94018i	0.178363	+	0.178363i
$489$	−1.24816	−	16.1286i	−0.0564439	−	0.729360i
$490$	1.17056	−	0.984403i	0.0528803	−	0.0444708i
$491$		−	6.45884i		−	0.291483i	−0.989323	−	0.145742i	$-0.953443\pi$
$491$		−	6.45884i		−	0.291483i	0.989323	−	0.145742i	$-0.0465568\pi$
$492$	−3.43137	+	4.00701i	−0.154698	+	0.180650i
$493$	−0.265146	+	0.265146i	−0.0119416	+	0.0119416i
$494$	12.1107			0.544887
$495$	1.36059	+	19.8900i	0.0611538	+	0.893989i
$496$	−6.33502			−0.284451
$497$	14.9944	−	14.9944i	0.672593	−	0.672593i
$498$	19.3955	−	22.6492i	0.869132	−	1.01494i
$499$			9.53761i			0.426962i	0.976947	+	0.213481i	$0.0684802\pi$
$499$			9.53761i			0.426962i	−0.976947	+	0.213481i	$0.931520\pi$
$500$	−10.8088	−	2.85813i	−0.483386	−	0.127819i
$501$	−0.992338	−	12.8228i	−0.0443344	−	0.572883i
$502$	−13.5208	−	13.5208i	−0.603464	−	0.603464i
$503$	−15.2096	−	15.2096i	−0.678161	−	0.678161i	0.281423	−	0.959584i	$-0.409194\pi$
$503$	−15.2096	−	15.2096i	−0.678161	−	0.678161i	−0.959584	+	0.281423i	$0.909194\pi$
$504$	8.21699	−	1.27946i	0.366014	−	0.0569917i
$505$	6.70506	+	0.579206i	0.298371	+	0.0257743i
$506$			2.97195i			0.132119i
$507$	12.4300	+	10.6443i	0.552034	+	0.472730i
$508$	−9.95020	+	9.95020i	−0.441469	+	0.441469i
$509$	27.1370			1.20282			0.601412	−	0.798939i	$-0.294605\pi$
$509$	27.1370			1.20282			0.601412	+	0.798939i	$0.294605\pi$
$510$	−0.849198	+	0.834157i	−0.0376031	+	0.0369371i
$511$	−15.9046			−0.703577
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	17.5580	−	28.4018i	0.775205	−	1.25397i
$514$			24.0535i			1.06096i
$515$	−3.70085	−	4.40069i	−0.163079	−	0.193918i
$516$	4.40057	−	0.340552i	0.193724	−	0.0149920i
$517$	0.592665	+	0.592665i	0.0260654	+	0.0260654i
$518$	−3.97242	−	3.97242i	−0.174538	−	0.174538i
$519$	−39.5113	+	3.05771i	−1.73435	+	0.134219i
$520$	0.362682	−	4.19851i	0.0159047	−	0.184117i
$521$			41.9658i			1.83855i	0.393611	+	0.919277i	$0.371226\pi$
$521$			41.9658i			1.83855i	−0.393611	+	0.919277i	$0.628774\pi$
$522$	−2.95543	−	2.15906i	−0.129356	−	0.0944994i
$523$	22.7710	−	22.7710i	0.995704	−	0.995704i	−0.00428643	−	0.999991i	$-0.501364\pi$
$523$	22.7710	−	22.7710i	0.995704	−	0.995704i	0.999991	+	0.00428643i	$0.00136442\pi$
$524$	−4.14724			−0.181173
$525$	−23.8978	−	2.27967i	−1.04298	−	0.0994928i
$526$	−17.4761			−0.761992
$527$	1.37678	−	1.37678i	0.0599736	−	0.0599736i
$528$	−3.90988	−	3.34819i	−0.170156	−	0.145711i
$529$			1.00000i			0.0434783i
$530$	2.49807	−	28.9184i	0.108509	−	1.25614i
$531$	−4.35256	−	27.9532i	−0.188885	−	1.21306i
$532$	12.5957	+	12.5957i	0.546094	+	0.546094i
$533$	4.05891	+	4.05891i	0.175811	+	0.175811i
$534$	−0.328279	−	4.24198i	−0.0142060	−	0.183568i
$535$	−20.6693	−	24.5779i	−0.893610	−	1.06259i
$536$			13.3086i			0.574844i
$537$	14.2049	−	16.5879i	0.612986	−	0.715820i
$538$	−14.2128	+	14.2128i	−0.612758	+	0.612758i
$539$	−2.03280			−0.0875591
$540$	−9.32045	−	6.93752i	−0.401088	−	0.298543i
$541$	8.43337			0.362579			0.181290	−	0.983430i	$-0.441973\pi$
$541$	8.43337			0.362579			0.181290	+	0.983430i	$0.441973\pi$
$542$	19.7054	−	19.7054i	0.846419	−	0.846419i
$543$	−1.97584	+	2.30730i	−0.0847912	+	0.0990157i
$544$		−	0.307349i		−	0.0131775i
$545$	7.17971	+	0.620208i	0.307545	+	0.0265668i
$546$	−0.698164	−	9.02157i	−0.0298787	−	0.386088i
$547$	−13.9532	−	13.9532i	−0.596597	−	0.596597i	0.342808	−	0.939405i	$-0.388622\pi$
$547$	−13.9532	−	13.9532i	−0.596597	−	0.596597i	−0.939405	+	0.342808i	$0.888622\pi$
$548$	−6.71805	−	6.71805i	−0.286981	−	0.286981i
$549$	−2.57196	−	16.5177i	−0.109769	−	0.704959i
$550$	8.54990	+	12.1537i	0.364569	+	0.518235i
$551$		−	7.83994i		−	0.333993i
$552$	−1.31559	−	1.12660i	−0.0559953	−	0.0479511i
$553$	28.2839	−	28.2839i	1.20275	−	1.20275i
$554$	−9.96921			−0.423551
$555$	−0.0701326	+	7.84883i	−0.00297696	+	0.333164i
$556$	−21.3303			−0.904607
$557$	−19.9924	+	19.9924i	−0.847106	+	0.847106i	−0.989771	−	0.142665i	$-0.954433\pi$
$557$	−19.9924	+	19.9924i	−0.847106	+	0.847106i	0.142665	+	0.989771i	$0.454433\pi$
$558$	15.3462	+	11.2110i	0.649657	+	0.474600i
$559$		−	4.80252i		−	0.203125i
$560$	4.74387	−	3.98945i	0.200465	−	0.168585i
$561$	1.57739	−	0.122071i	0.0665974	−	0.00515386i
$562$	−11.1642	−	11.1642i	−0.470934	−	0.470934i
$563$	−31.0332	−	31.0332i	−1.30789	−	1.30789i	−0.922935	−	0.384957i	$-0.874216\pi$
$563$	−31.0332	−	31.0332i	−1.30789	−	1.30789i	−0.384957	−	0.922935i	$-0.625784\pi$
$564$	−0.487019	+	0.0376896i	−0.0205072	+	0.00158702i
$565$	9.02716	−	7.59158i	0.379776	−	0.319380i
$566$			18.6737i			0.784912i
$567$	−22.1694	−	11.4421i	−0.931027	−	0.480522i
$568$	5.40925	−	5.40925i	0.226967	−	0.226967i
$569$	−30.3632			−1.27289			−0.636447	−	0.771321i	$-0.719596\pi$
$569$	−30.3632			−1.27289			−0.636447	+	0.771321i	$0.719596\pi$
$570$	0.222376	−	24.8870i	0.00931431	−	1.04240i
$571$	−13.6437			−0.570973			−0.285486	−	0.958383i	$-0.592155\pi$
$571$	−13.6437			−0.570973			−0.285486	+	0.958383i	$0.592155\pi$
$572$	−3.96052	+	3.96052i	−0.165598	+	0.165598i
$573$	−35.4269	−	30.3375i	−1.47998	−	1.26737i
$574$			8.44292i			0.352401i
$575$	2.87686	+	4.08946i	0.119973	+	0.170542i
$576$	2.96428	−	0.461565i	0.123512	−	0.0192319i
$577$	29.2454	+	29.2454i	1.21750	+	1.21750i	0.968503	+	0.249001i	$0.0801021\pi$
$577$	29.2454	+	29.2454i	1.21750	+	1.21750i	0.249001	+	0.968503i	$0.419898\pi$
$578$	−11.9540	−	11.9540i	−0.497222	−	0.497222i
$579$	2.06605	+	26.6972i	0.0858620	+	1.10950i
$580$	−2.71793	−	0.234784i	−0.112856	−	0.00974888i
$581$		−	47.7228i		−	1.97988i
$582$	−14.3193	+	16.7215i	−0.593553	+	0.693127i
$583$	−27.2791	+	27.2791i	−1.12979	+	1.12979i
$584$	−5.73758			−0.237423
$585$	−8.30862	+	9.52880i	−0.343519	+	0.393968i
$586$	−9.81215			−0.405336
$587$	−30.7364	+	30.7364i	−1.26863	+	1.26863i	−0.321830	+	0.946798i	$0.604298\pi$
$587$	−30.7364	+	30.7364i	−1.26863	+	1.26863i	−0.946798	+	0.321830i	$0.895702\pi$
$588$	0.770587	−	0.899860i	0.0317785	−	0.0371096i
$589$			40.7093i			1.67740i
$590$	−13.5716	−	16.1380i	−0.558734	−	0.664392i
$591$	0.374079	+	4.83380i	0.0153876	+	0.198836i
$592$	−1.43305	−	1.43305i	−0.0588980	−	0.0588980i
$593$	24.9741	+	24.9741i	1.02557	+	1.02557i	0.999665	+	0.0259005i	$0.00824531\pi$
$593$	24.9741	+	24.9741i	1.02557	+	1.02557i	0.0259005	+	0.999665i	$0.491755\pi$
$594$	3.54620	+	15.0300i	0.145502	+	0.616690i
$595$	−0.163956	+	1.89800i	−0.00672154	+	0.0778105i
$596$		−	2.04707i		−	0.0838514i
$597$	−20.9037	−	17.9007i	−0.855531	−	0.732627i
$598$	−1.33263	+	1.33263i	−0.0544953	+	0.0544953i
$599$	35.3695			1.44516			0.722579	−	0.691288i	$-0.242956\pi$
$599$	35.3695			1.44516			0.722579	+	0.691288i	$0.242956\pi$
$600$	−8.62112	−	0.822390i	−0.351956	−	0.0335739i
$601$	36.5041			1.48903			0.744517	−	0.667604i	$-0.232680\pi$
$601$	36.5041			1.48903			0.744517	+	0.667604i	$0.232680\pi$
$602$	4.99486	−	4.99486i	0.203575	−	0.203575i
$603$	23.5521	−	32.2393i	0.959114	−	1.31288i
$604$			2.64015i			0.107426i
$605$	−0.417117	+	4.82867i	−0.0169582	+	0.196313i
$606$	5.19752	−	0.402227i	0.211135	−	0.0163394i
$607$	22.0917	+	22.0917i	0.896673	+	0.896673i	0.995140	−	0.0984669i	$-0.0313939\pi$
$607$	22.0917	+	22.0917i	0.896673	+	0.896673i	−0.0984669	+	0.995140i	$0.531394\pi$
$608$	4.54391	+	4.54391i	0.184280	+	0.184280i
$609$	−5.84017	+	0.451961i	−0.236656	+	0.0183144i
$610$	−8.01956	−	9.53607i	−0.324702	−	0.386104i
$611$			0.531504i			0.0215024i
$612$	−0.543912	+	0.744535i	−0.0219863	+	0.0300960i
$613$	16.7926	−	16.7926i	0.678246	−	0.678246i	−0.281357	−	0.959603i	$-0.590784\pi$
$613$	16.7926	−	16.7926i	0.678246	−	0.678246i	0.959603	+	0.281357i	$0.0907845\pi$
$614$	11.8644			0.478808
$615$	8.41542	−	8.26636i	0.339343	−	0.333332i
$616$	−8.23826			−0.331929
$617$	26.9980	−	26.9980i	1.08690	−	1.08690i	0.0910505	−	0.995846i	$-0.470978\pi$
$617$	26.9980	−	26.9980i	1.08690	−	1.08690i	0.995846	−	0.0910505i	$-0.0290225\pi$
$618$	−3.38301	−	2.89701i	−0.136085	−	0.116535i
$619$			31.5835i			1.26945i	0.772739	+	0.634724i	$0.218886\pi$
$619$			31.5835i			1.26945i	−0.772739	+	0.634724i	$0.781114\pi$
$620$	14.1130	+	1.21913i	0.566791	+	0.0489614i
$621$	1.19322	+	5.05729i	0.0478823	+	0.202942i
$622$	−16.0579	−	16.0579i	−0.643865	−	0.643865i
$623$	−4.81485	−	4.81485i	−0.192903	−	0.192903i
$624$	−0.251863	−	3.25453i	−0.0100826	−	0.130286i
$625$	23.5296	+	8.44734i	0.941184	+	0.337894i
$626$		−	26.9989i		−	1.07909i
$627$	−21.5157	+	25.1251i	−0.859254	+	1.00340i
$628$	0.750993	−	0.750993i	0.0299679	−	0.0299679i
$629$	0.622887			0.0248361
$630$	−18.5518	+	1.26905i	−0.739121	+	0.0505600i
$631$	−27.4404			−1.09239			−0.546193	−	0.837659i	$-0.683924\pi$
$631$	−27.4404			−1.09239			−0.546193	+	0.837659i	$0.683924\pi$
$632$	10.2034	−	10.2034i	0.405870	−	0.405870i
$633$	12.8327	−	14.9855i	0.510055	−	0.595622i
$634$		−	0.0389545i		−	0.00154708i
$635$	24.0816	−	20.2519i	0.955650	−	0.803673i
$636$	−1.73477	−	22.4165i	−0.0687883	−	0.888872i
$637$	−0.911514	−	0.911514i	−0.0361155	−	0.0361155i
$638$	2.56386	+	2.56386i	0.101504	+	0.101504i
$639$	−22.6762	+	3.53090i	−0.897058	+	0.139680i
$640$	1.71135	−	1.43919i	0.0676470	−	0.0568892i
$641$		−	1.78898i		−	0.0706606i	−0.999376	−	0.0353303i	$-0.988752\pi$
$641$		−	1.78898i		−	0.0706606i	0.999376	−	0.0353303i	$-0.0112483\pi$
$642$	−18.8941	−	16.1798i	−0.745691	−	0.638566i
$643$	24.6839	−	24.6839i	0.973437	−	0.973437i	−0.0262188	−	0.999656i	$-0.508347\pi$
$643$	24.6839	−	24.6839i	0.973437	−	0.973437i	0.999656	+	0.0262188i	$0.00834667\pi$
$644$	−2.77200			−0.109232
$645$	−9.86899	−	0.0881836i	−0.388591	−	0.00347222i
$646$	−1.97505			−0.0777072
$647$	2.36727	−	2.36727i	0.0930671	−	0.0930671i	−0.659040	−	0.752108i	$-0.729037\pi$
$647$	2.36727	−	2.36727i	0.0930671	−	0.0930671i	0.752108	+	0.659040i	$0.229037\pi$
$648$	−7.99761	−	4.12773i	−0.314176	−	0.162153i
$649$			28.0255i			1.10010i
$650$	−1.61594	+	9.28353i	−0.0633826	+	0.364130i
$651$	30.3254	−	2.34683i	1.18854	−	0.0919794i
$652$	−6.60415	−	6.60415i	−0.258639	−	0.258639i
$653$	2.10868	+	2.10868i	0.0825189	+	0.0825189i	0.747161	−	0.664643i	$-0.231416\pi$
$653$	2.10868	+	2.10868i	0.0825189	+	0.0825189i	−0.664643	+	0.747161i	$0.731416\pi$
$654$	5.56545	−	0.430701i	0.217626	−	0.0168417i
$655$	9.23911	+	0.798106i	0.361002	+	0.0311846i
$656$			3.04579i			0.118918i
$657$	13.8989	+	10.1537i	0.542249	+	0.396134i
$658$	−0.552791	+	0.552791i	−0.0215500	+	0.0215500i
$659$	40.8784			1.59240			0.796199	−	0.605035i	$-0.206841\pi$
$659$	40.8784			1.59240			0.796199	+	0.605035i	$0.206841\pi$
$660$	8.06598	+	8.21143i	0.313968	+	0.319629i
$661$	17.8125			0.692828			0.346414	−	0.938082i	$-0.387399\pi$
$661$	17.8125			0.692828			0.346414	+	0.938082i	$0.387399\pi$
$662$	−0.743610	+	0.743610i	−0.0289012	+	0.0289012i
$663$	0.762041	+	0.652567i	0.0295952	+	0.0253436i
$664$		−	17.2160i		−	0.668111i
$665$	−25.6365	−	30.4844i	−0.994140	−	1.18213i
$666$	0.935427	+	6.00753i	0.0362471	+	0.232787i
$667$	0.862686	+	0.862686i	0.0334033	+	0.0334033i
$668$	−5.25056	−	5.25056i	−0.203150	−	0.203150i
$669$	1.97842	+	25.5648i	0.0764900	+	0.988392i
$670$	2.56114	−	29.6485i	0.0989455	−	1.14542i
$671$			16.5605i			0.639310i
$672$	3.12292	−	3.64682i	0.120469	−	0.140679i
$673$	13.7420	−	13.7420i	0.529714	−	0.529714i	−0.390773	−	0.920487i	$-0.627792\pi$
$673$	13.7420	−	13.7420i	0.529714	−	0.529714i	0.920487	+	0.390773i	$0.127792\pi$
$674$	14.1764			0.546054
$675$	19.4288	+	17.2489i	0.747813	+	0.663909i
$676$	9.44819			0.363392
$677$	1.91031	−	1.91031i	0.0734192	−	0.0734192i	−0.669444	−	0.742863i	$-0.733467\pi$
$677$	1.91031	−	1.91031i	0.0734192	−	0.0734192i	0.742863	+	0.669444i	$0.233467\pi$
$678$	5.94265	−	6.93959i	0.228226	−	0.266513i
$679$			35.2328i			1.35211i
$680$	−0.0591471	+	0.684704i	−0.00226819	+	0.0262572i
$681$	3.05537	+	39.4810i	0.117082	+	1.51292i
$682$	−13.3130	−	13.3130i	−0.509780	−	0.509780i
$683$	−33.5563	−	33.5563i	−1.28400	−	1.28400i	−0.938374	−	0.345623i	$-0.887668\pi$
$683$	−33.5563	−	33.5563i	−1.28400	−	1.28400i	−0.345623	−	0.938374i	$-0.612332\pi$
$684$	−2.96605	−	19.0487i	−0.113410	−	0.728344i
$685$	13.6735	+	16.2591i	0.522436	+	0.621229i
$686$			17.5080i			0.668458i
$687$	−21.0886	−	18.0590i	−0.804581	−	0.688996i
$688$	1.80190	−	1.80190i	0.0686966	−	0.0686966i
$689$	−24.4641			−0.932006
$690$	2.71403	+	2.76297i	0.103322	+	0.105185i
$691$	−27.4000			−1.04234			−0.521172	−	0.853451i	$-0.674505\pi$
$691$	−27.4000			−1.04234			−0.521172	+	0.853451i	$0.674505\pi$
$692$	−16.1787	+	16.1787i	−0.615020	+	0.615020i
$693$	19.9567	+	14.5791i	0.758092	+	0.553816i
$694$			25.8642i			0.981790i
$695$	47.5191	+	4.10486i	1.80250	+	0.155706i
$696$	−2.10684	+	0.163045i	−0.0798596	+	0.00618020i
$697$	−0.661937	−	0.661937i	−0.0250727	−	0.0250727i
$698$	20.2968	+	20.2968i	0.768247	+	0.768247i
$699$	−10.1266	+	0.783682i	−0.383024	+	0.0296416i
$700$	−11.3360	+	7.97466i	−0.428460	+	0.301414i
$701$		−	17.7628i		−	0.670893i	−0.942059	−	0.335446i	$-0.891113\pi$
$701$		−	17.7628i		−	0.670893i	0.942059	−	0.335446i	$-0.108887\pi$
$702$	−5.14938	+	8.32963i	−0.194351	+	0.314381i
$703$	−9.20888	+	9.20888i	−0.347319	+	0.347319i
$704$	−2.97195			−0.112010
$705$	1.09222	+	0.00975945i	0.0411354	+	0.000367562i
$706$	−14.7901			−0.556631
$707$	5.89944	−	5.89944i	0.221871	−	0.221871i
$708$	−12.4060	−	10.6238i	−0.466247	−	0.399267i
$709$			25.1030i			0.942763i	0.881929	+	0.471382i	$0.156245\pi$
$709$			25.1030i			0.942763i	−0.881929	+	0.471382i	$0.843755\pi$
$710$	−13.0915	+	11.0096i	−0.491316	+	0.413183i
$711$	−42.7740	+	6.66031i	−1.60415	+	0.249781i
$712$	−1.73696	−	1.73696i	−0.0650953	−	0.0650953i
$713$	−4.47954	−	4.47954i	−0.167760	−	0.167760i
$714$	0.113858	+	1.47126i	0.00426104	+	0.0550606i
$715$	9.58530	−	8.06095i	0.358470	−	0.301463i
$716$		−	12.6087i		−	0.471209i
$717$	33.5338	−	39.1594i	1.25234	−	1.46244i
$718$	7.38357	−	7.38357i	0.275552	−	0.275552i
$719$	7.11858			0.265478			0.132739	−	0.991151i	$-0.457623\pi$
$719$	7.11858			0.265478			0.132739	+	0.991151i	$0.457623\pi$
$720$	−6.69256	+	0.457809i	−0.249417	+	0.0170615i
$721$	−7.12813			−0.265466
$722$	15.7644	−	15.7644i	0.586692	−	0.586692i
$723$	−20.4537	+	23.8850i	−0.760681	+	0.888292i
$724$			1.75381i			0.0651799i
$725$	6.00975	+	1.04609i	0.223196	+	0.0388508i
$726$	0.289665	+	3.74301i	0.0107505	+	0.138916i
$727$	−21.0233	−	21.0233i	−0.779711	−	0.779711i	0.200070	−	0.979782i	$-0.435883\pi$
$727$	−21.0233	−	21.0233i	−0.779711	−	0.779711i	−0.979782	+	0.200070i	$0.935883\pi$
$728$	−3.69405	−	3.69405i	−0.136911	−	0.136911i
$729$	12.0689	+	24.1524i	0.446998	+	0.894535i
$730$	12.7820	+	1.10415i	0.473083	+	0.0408666i
$731$			0.783208i			0.0289680i
$732$	−7.33081	−	6.27767i	−0.270955	−	0.232030i
$733$	−8.70985	+	8.70985i	−0.321706	+	0.321706i	−0.849421	−	0.527715i	$-0.823049\pi$
$733$	−8.70985	+	8.70985i	−0.321706	+	0.321706i	0.527715	+	0.849421i	$0.323049\pi$
$734$	−16.0003			−0.590580
$735$	−1.88986	+	1.85639i	−0.0697086	+	0.0684739i
$736$	−1.00000			−0.0368605
$737$	−27.9679	+	27.9679i	−1.03021	+	1.03021i
$738$	5.39009	−	7.37823i	0.198412	−	0.271596i
$739$		−	13.3134i		−	0.489743i	−0.969556	−	0.244871i	$-0.921254\pi$
$739$		−	13.3134i		−	0.489743i	0.969556	−	0.244871i	$-0.0787458\pi$
$740$	2.91673	+	3.46829i	0.107221	+	0.127497i
$741$	−20.9138	+	1.61849i	−0.768289	+	0.0594566i
$742$	−25.4438	−	25.4438i	−0.934072	−	0.934072i
$743$	−31.8345	−	31.8345i	−1.16789	−	1.16789i	−0.982702	−	0.185193i	$-0.940709\pi$
$743$	−31.8345	−	31.8345i	−1.16789	−	1.16789i	−0.185193	−	0.982702i	$-0.559291\pi$
$744$	10.9399	−	0.846618i	0.401075	−	0.0310385i
$745$	−0.393944	+	4.56041i	−0.0144330	+	0.167081i
$746$		−	28.6369i		−	1.04847i
$747$	−30.4669	+	41.7047i	−1.11473	+	1.52590i
$748$	0.645891	−	0.645891i	0.0236161	−	0.0236161i
$749$	−39.8106			−1.45465
$750$	19.0476	+	3.49117i	0.695521	+	0.127479i
$751$	1.87068			0.0682622			0.0341311	−	0.999417i	$-0.489134\pi$
$751$	1.87068			0.0682622			0.0341311	+	0.999417i	$0.489134\pi$
$752$	−0.199419	+	0.199419i	−0.00727207	+	0.00727207i
$753$	25.1559	+	21.5420i	0.916732	+	0.785035i
$754$			2.29928i			0.0837349i
$755$	0.508077	−	5.88165i	0.0184908	−	0.214055i
$756$	−14.0188	+	3.30761i	−0.509860	+	0.120297i
$757$	−4.50446	−	4.50446i	−0.163717	−	0.163717i	0.620494	−	0.784211i	$-0.286932\pi$
$757$	−4.50446	−	4.50446i	−0.163717	−	0.163717i	−0.784211	+	0.620494i	$0.786932\pi$
$758$	22.2485	+	22.2485i	0.808102	+	0.808102i
$759$	−0.397175	−	5.13223i	−0.0144165	−	0.186288i
$760$	−9.24836	−	10.9972i	−0.335473	−	0.398912i
$761$		−	29.5482i		−	1.07112i	−0.844497	−	0.535561i	$-0.820100\pi$
$761$		−	29.5482i		−	1.07112i	0.844497	−	0.535561i	$-0.179900\pi$
$762$	15.8531	−	18.5126i	0.574298	−	0.670642i
$763$	6.31706	−	6.31706i	0.228693	−	0.228693i
$764$	−26.9285			−0.974238
$765$	1.35499	−	1.55398i	0.0489898	−	0.0561843i
$766$	7.21387			0.260648
$767$	−12.5667	+	12.5667i	−0.453757	+	0.453757i
$768$	1.12660	−	1.31559i	0.0406525	−	0.0474723i
$769$			14.7558i			0.532107i	0.963958	+	0.266054i	$0.0857199\pi$
$769$			14.7558i			0.532107i	−0.963958	+	0.266054i	$0.914280\pi$
$770$	18.3530	+	1.58539i	0.661395	+	0.0571336i
$771$	−3.21454	−	41.5378i	−0.115769	−	1.49595i
$772$	10.9317	+	10.9317i	0.393439	+	0.393439i
$773$	9.22983	+	9.22983i	0.331974	+	0.331974i	0.853336	−	0.521362i	$-0.174576\pi$
$773$	9.22983	+	9.22983i	0.331974	+	0.331974i	−0.521362	+	0.853336i	$0.674576\pi$
$774$	−7.55377	+	1.17619i	−0.271515	+	0.0422773i
$775$	−31.2059	−	5.43188i	−1.12095	−	0.195119i
$776$			12.7102i			0.456270i
$777$	7.39080	+	6.32905i	0.265144	+	0.227053i
$778$	−12.9858

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.12660 - 1.31559i) q^{3} -1.00000i q^{4} +(-0.192443 + 2.22777i) q^{5} +(0.133641 + 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.461565 - 2.96428i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.12660 - 1.31559i) q^{3} -1.00000i q^{4} +(-0.192443 + 2.22777i) q^{5} +(0.133641 + 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.461565 - 2.96428i) q^{9} +(-1.43919 - 1.71135i) q^{10} +2.97195i q^{11} +(-1.31559 - 1.12660i) q^{12} +(-1.33263 + 1.33263i) q^{13} -2.77200 q^{14} +(2.71403 + 2.76297i) q^{15} -1.00000 q^{16} +(0.217329 - 0.217329i) q^{17} +(2.42244 + 1.76969i) q^{18} +6.42606i q^{19} +(2.22777 + 0.192443i) q^{20} +(4.78694 - 0.370453i) q^{21} +(-2.10149 - 2.10149i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(1.72689 - 0.133641i) q^{24} +(-4.92593 - 0.857436i) q^{25} -1.88462i q^{26} +(-4.41978 - 2.73231i) q^{27} +(1.96010 - 1.96010i) q^{28} -1.22002 q^{29} +(-3.87283 - 0.0346053i) q^{30} +6.33502 q^{31} +(0.707107 - 0.707107i) q^{32} +(3.90988 + 3.34819i) q^{33} +0.307349i q^{34} +(-4.74387 + 3.98945i) q^{35} +(-2.96428 + 0.461565i) q^{36} +(1.43305 + 1.43305i) q^{37} +(-4.54391 - 4.54391i) q^{38} +(0.251863 + 3.25453i) q^{39} +(-1.71135 + 1.43919i) q^{40} -3.04579i q^{41} +(-3.12292 + 3.64682i) q^{42} +(-1.80190 + 1.80190i) q^{43} +2.97195 q^{44} +(6.69256 - 0.457809i) q^{45} +1.00000 q^{46} +(0.199419 - 0.199419i) q^{47} +(-1.12660 + 1.31559i) q^{48} +0.683996i q^{49} +(4.08946 - 2.87686i) q^{50} +(-0.0410744 - 0.530758i) q^{51} +(1.33263 + 1.33263i) q^{52} +(9.17886 + 9.17886i) q^{53} +(5.05729 - 1.19322i) q^{54} +(-6.62083 - 0.571930i) q^{55} +2.77200i q^{56} +(8.45408 + 7.23957i) q^{57} +(0.862686 - 0.862686i) q^{58} +9.43000 q^{59} +(2.76297 - 2.71403i) q^{60} +5.57225 q^{61} +(-4.47954 + 4.47954i) q^{62} +(4.90558 - 6.71501i) q^{63} +1.00000i q^{64} +(-2.71234 - 3.22525i) q^{65} +(-5.13223 + 0.397175i) q^{66} +(9.41060 + 9.41060i) q^{67} +(-0.217329 - 0.217329i) q^{68} +(-1.72689 + 0.133641i) q^{69} +(0.533451 - 6.17539i) q^{70} -7.64983i q^{71} +(1.76969 - 2.42244i) q^{72} +(-4.05708 + 4.05708i) q^{73} -2.02664 q^{74} +(-6.67757 + 5.51453i) q^{75} +6.42606 q^{76} +(-5.82533 + 5.82533i) q^{77} +(-2.47940 - 2.12321i) q^{78} -14.4298i q^{79} +(0.192443 - 2.22777i) q^{80} +(-8.57391 + 2.73642i) q^{81} +(2.15370 + 2.15370i) q^{82} +(-12.1736 - 12.1736i) q^{83} +(-0.370453 - 4.78694i) q^{84} +(0.442336 + 0.525982i) q^{85} -2.54827i q^{86} +(-1.37447 + 1.60505i) q^{87} +(-2.10149 + 2.10149i) q^{88} -2.45643 q^{89} +(-4.40864 + 5.05608i) q^{90} -5.22418 q^{91} +(-0.707107 + 0.707107i) q^{92} +(7.13701 - 8.33431i) q^{93} +0.282021i q^{94} +(-14.3158 - 1.23665i) q^{95} +(-0.133641 - 1.72689i) q^{96} +(8.98748 + 8.98748i) q^{97} +(-0.483658 - 0.483658i) q^{98} +(8.80970 - 1.37175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \)	\( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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